Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function

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dc.contributor.author Thomas, Michael en
dc.contributor.author Wilson, AJ en
dc.contributor.author Corballis, Michael en
dc.contributor.author Lim, VK en
dc.contributor.author Yoon, C en
dc.date.accessioned 2012-03-09T01:44:49Z en
dc.date.issued 2010 en
dc.identifier.citation ZDM The International Journal on Mathematics Education 5:607-619 2010 en
dc.identifier.issn 1863-9704 en
dc.identifier.uri http://hdl.handle.net/2292/13609 en
dc.description.abstract Using traditional educational research methods, it is difficult to assess students’ understanding of mathematical concepts, even though qualitative methods such as task observation and interviews provide some useful information. It has now become possible to use functional magnetic resonance imaging (fMRI) to observe brain activity whilst students think about mathematics, although much of this work has concentrated on number. In this study, we used fMRI to examine brain activity whilst ten university students translated between graphical and algebraic formats of both linear and quadratic mathematical functions. Consistent with previous studies on the representation of number, this task elicited activity in the intra-parietal sulcus, as well as in the inferior frontal gyrus.Wealso analysed qualitative data on participants’ introspection of strategies employed when reasoning about function. Expert participants focused more on key properties of functions when translating between formats than did novices. Implications for the teaching and learning of functions are discussed, including the relationship of function properties to difficulties in conversion from algebraic to graphical representation systems and vice versa, the desirability of teachers focusing attention on function properties, and the importance of integrating graphical and algebraic function instruction. en
dc.publisher Springer Verlag en
dc.relation.ispartofseries ZDM International Journal on Mathematics Education en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from: http://www.sherpa.ac.uk/romeo/issn/1863-9690/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function en
dc.type Journal Article en
dc.identifier.doi 10.1007/s11858-010-0272-7 en
pubs.begin-page 607 en
pubs.volume 5 en
dc.rights.holder Copyright: Springer Verlag en
pubs.end-page 619 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article en
pubs.elements-id 87428 en
pubs.record-created-at-source-date 2010-09-01 en

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